Space Charge in High Current Lower Energy Electron Bunches

Transcription

1 Space Charge in High Current Lower Energy Electron Bunches DESY Workshop June 20th 2006, S. Becker, F. Grüner, U. Schramm, R. Sousa, T. Eichner, D. Habs Self acceleration: Results from CSRtrack vs. GPT vs. HOMDYN Self acceleration: Theoretically GPT: The applied calculation method Longitudinal phase space Spatial distribution Considering slices

2 Simulation Extreme case: PIC-Simulations -> σ x = σ y = σ z = 1 µm Charge: 1.25 nc -> I = 150 ka Initial distribution: Gaussian Comparison between CSRtrack and GPT

3 Self Acceleration CSRtrack GPT Initial distribution After a free drift of approx. 20mm Gain of kinetic energy of approx. 20%

4 Self Acceleration Pz_[beta*g] HOMDYN results do not comply to CSRtrack and GPT, predicting strong debunching. Locking for the origin of these contradictions is work in progress HSPACE.OUT DZ_[mm] from FLS workshop May 18 th 2006 by Luca Serafini - INFN/MI

5 Self Acceleration Electron's rest frame: Potential energy leads to a mass defect: E pot = m d c 2 Total energy in the electrons' mean rest frame: E ' = E 0 E pot = m 0 c 2 E pot = m 0 m d c 2 E ' = m' c 2 = ' m 0 c 2 after potential energy released Potential energy in average is estimated to be of the order of 100 kev / electron Mean Lorentz factor due to Coulomb explosion: ' = 1 m d m 0 Laboratory frame: Electron bunch is leaves the bubble with 0 Total energy: E = 0 m' c 2 = 0 m 0 c 2 1 m d m 0 E = 0 ' m 0 c 2 = m 0 c 2 after potential energy released

6 GPT GPT adapts time steps dynamically Calculation precision is defined by relative momentum changes stepwise Space charge is considered point to point using Lorentz transformation. Calculation time t ~ N² For equation of motion: From Lorentz transformations: Interaction in rest frame:

7 GPT- Energy Conservation Our personal Lackmustest for the evaluation of GPT results

8 Experimental Overview Quadrupole Triplet Field gradient 500 T/m Gas Jet Aperture Electron Beam Peak energy 130 MeV Undulator Period 5mm K ~ 0.5 FEL Radiation at VUV Aperture TW Laser Grating Spectrometer Acceleration fields in the order of TV/m

9 Longitudinal Phase Space Evolution from hat to an almost linear energy chirp

10 Longitudinal Phase Space θ L... length of free (divergent) drift Δs... difference of propagation distance of axial electrons compared to electrons of angle θ Criteria for the phase space to become a linear energy shift: -Axial electron propagates with 0 -Electron at angle θ propagates with 1 0 s ~ 1 cos 2 L z s L phase space becomes linear chirp for 0

11 Longitudinal Phase Space Coulomb explosion of resting electrons of a respective bunch yields: ' = 0.7 = ' mrad This θ is smaller than expected, especially after collimating the beam

12 Spatial Distribution After refocusing, the spacial shape of the bunch reminds of... a fish...

13 Spatial Distribution The presented calculation is far from being optimized. The fish in this case is not slim but rather looks like a hammerhead shark. Optimization using linear beam optics is not possible, as the beam keeps gaining kinetic energy while propagating though the lens Optimization hence is work in progress as being very time consuming Longitudinal beam prolongation slicing

14 Slices Just qualitatively, as beam is not optimized!!!

15 Slices Just qualitatively, as beam is not optimized!!!

16 Summary Self acceleration: Results from CSRtrack vs. GPT vs. HOMDYN Self acceleration: Theoretically GPT: The applied calculation method Longitudinal phase space Spatial distribution Considering slices - qualitatively